Question: (15 points) A women has 9 close friends.

(a) In how many ways can she invite five of these to dinner? Explain.

(b) Repeat part (a) with the added stipulation that two of her friends do not like each other so that if she invites one of them she cannot invite the other. Explain.

(c) Repeat part (a), assuming that the nine friends consist of five single people and 2 married couples. If she invites a husband or wife she must invite the spouse. Explain.